I think that you're both right. Generally speaking, killing animals is seen karmically as a very negative action that can lead to rebirth in a hell realm, as it says in the Close Mindfulness Sutra and elsewhere, and hunting is viewed in a particularly negative light in the sutras. However, one can imagine unusual mitigating circumstances. If one were to kill an animal without bearing the animal any hostility, solely out of compassion, to feed one's family, because one had no other option, then surely it would be karmically different from killing out of craving or greed and a lack of compassion for other creatures. And as Adamantine points out, regret diminishes the karmic impact of an action. I don't suppose that compassionate killing is a common occurrence, however.
There are sutras, such as the Candra-pradīpa Sūtra and the Upāya-kauśalya Sūtra, among others, that teach that when the motive is compassion, there is no fault for a bodhisattva in breaking a precept. As Ven. Indrajala mentioned, the Yogācārabhūmi Śāstra also teaches this. Śāntideva takes this view in his Compendium of Training. (In the Gelug lineage it is specified that one must have actualized bodhicitta and must be holding the Bodhisattva Vow to manage this, however.) There seem to be nearly always exceptions to the rule in Mahāyāna, although some sutras, such as the second century Bodhisattva-Piṭāka Sūtra, take a stricter view, permitting no exceptions to the precepts.
Having said this, I think it still makes sense to speak about certain deeds, such as killing beings, as being karmically highly negative and to be discouraged, generally speaking, and others, such as giving, being karmically highly positive and to be encouraged, generally speaking. It is helpful to offer general guidelines, though we could with some justification say, "It all depends." I think we would all agree that Buddhism teaches that giving is good and an important Buddhist practice, however, once again, this is a simplification. There are exceptions. The Akṣayamati Sūtra points out that giving is non-virtuous if one is giving something harmful, if one gives with hostility or contempt, if one gives less than one promised, etc. It is still a good policy to encourage giving.
EDIT: I'm a bit sleepy at the moment, so I hope this is coherent.
namo bhagavate śākyamunaye tathāgatāyārhate samyaksaṁbuddhāya | namaḥ sarvabuddhabodhisattvebhyaḥ ||
"Bodhisattva-mahāsattvas love all beings in the world equally, as if each were their only child..." Buddhāvataṃsakamahāvaipulya Sūtra